SRC/zheevd.f(3)

NAME
SRC/zheevd.f

SYNOPSIS

  Functions/Subroutines
subroutine zheevd (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)
ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Function/Subroutine Documentation

  subroutine zheevd (character jobz, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) w, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)

ZHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Purpose:

    !>
    !> ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a
    !> complex Hermitian matrix A.  If eigenvectors are desired, it uses a
    !> divide and conquer algorithm.
    !>
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only;
    !>          = 'V':  Compute eigenvalues and eigenvectors.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA, N)
    !>          On entry, the Hermitian matrix A.  If UPLO = 'U', the
    !>          leading N-by-N upper triangular part of A contains the
    !>          upper triangular part of the matrix A.  If UPLO = 'L',
    !>          the leading N-by-N lower triangular part of A contains
    !>          the lower triangular part of the matrix A.
    !>          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
    !>          orthonormal eigenvectors of the matrix A.
    !>          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
    !>          or the upper triangle (if UPLO='U') of A, including the
    !>          diagonal, is destroyed.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (N)
    !>          If INFO = 0, the eigenvalues in ascending order.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The length of the array WORK.
    !>          If N <= 1,                LWORK must be at least 1.
    !>          If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1.
    !>          If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + N**2.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal sizes of the WORK, RWORK and
    !>          IWORK arrays, returns these values as the first entries of
    !>          the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
    !>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
    !>

    LRWORK

    !>          LRWORK is INTEGER
    !>          The dimension of the array RWORK.
    !>          If N <= 1,                LRWORK must be at least 1.
    !>          If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
    !>          If JOBZ  = 'V' and N > 1, LRWORK must be at least
    !>                         1 + 5*N + 2*N**2.
    !>
    !>          If LRWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the optimal sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
    !>

    LIWORK

    !>          LIWORK is INTEGER
    !>          The dimension of the array IWORK.
    !>          If N <= 1,                LIWORK must be at least 1.
    !>          If JOBZ  = 'N' and N > 1, LIWORK must be at least 1.
    !>          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the optimal sizes of the WORK, RWORK
    !>          and IWORK arrays, returns these values as the first entries
    !>          of the WORK, RWORK and IWORK arrays, and no error message
    !>          related to LWORK or LRWORK or LIWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i and JOBZ = 'N', then the algorithm failed
    !>                to converge; i off-diagonal elements of an intermediate
    !>                tridiagonal form did not converge to zero;
    !>                if INFO = i and JOBZ = 'V', then the algorithm failed
    !>                to compute an eigenvalue while working on the submatrix
    !>                lying in rows and columns INFO/(N+1) through
    !>                mod(INFO,N+1).
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:
    Modified description of INFO. Sven, 16 Feb 05.

Contributors:
    Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 196 of file zheevd.f.

Author

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